Differentiate y=x^2+5x+3?

2 Answers
Apr 27, 2018

$2 x + 5$

Explanation:

Given: $y = {x}^{2} + 5 x + 3$.

Differentiate using the power rule, $\frac{d}{\mathrm{dx}} \left({a}^{x}\right) = x {a}^{x - 1} , x \ne - 1$ and the constant rule, $\frac{d}{\mathrm{dx}} \left(a\right) = 0 , a \in \mathbb{R}$.

We get:

$y ' = 2 x + 5 + 0$

$= 2 x + 5$

Apr 27, 2018

$\frac{d}{\mathrm{dx}} \left({x}^{2} + 5 x + 3\right) = 2 x + 5$

Explanation:

Derivative of any polynomial ${x}^{a} = a \cdot {x}^{a - 1}$.

Using this formula with the sum rule gives us-

Derivative of ${x}^{2} + 5 x + 3 = \frac{d}{\mathrm{dx}} \left({x}^{2}\right) + \frac{d}{\mathrm{dx}} 5 x + \frac{d}{\mathrm{dx}} 3$

=$2 x + 5 + 0$(derivative of constant is 0)

=$2 x + 5$